There are existing conventional filter for separating an optical signal having a specific wavelength .lambda..sub.o among optical signals having multiplexed wavelengths. For example, the literature (1) entitled "IEEE Communication Magazine", Pages P. 53 to P. 63, published Oct., 1989 discloses filters is divided into four classes, namely: (a) Fabry-Perot type; (b) Mach-Zehnder type; (c) mode conversion type; and (d) Bragg reflection type. Assuming that the transmission wavelength .lambda..sub.o is varied from a designed standard wavelength .lambda. to .lambda.+.DELTA..lambda., the filters of the type of a, b and d have the wavelength variation amount .DELTA..lambda. expressed in formula (1) while the filter of the type c has the wavelength variation amount .DELTA..lambda. expressed in formula (2). ##EQU1## where .DELTA.n: amount of refractive index which can be electrically varied by a waveguide of the filter
n: refractive index of the waveguide of the filter PA1 .delta.n: refractive index difference between modes e.g. refractive index difference between TM mode and TE mode.
The wavelength .lambda. is generally determined by shapes, dimensions, materials and the like of the components of the filter and forms a constant. However, since a filter utilizing an acousto-optical effect among the c-type filters can electrically vary the cycle of gratings for converting the modes of the light, the designed standard wavelength can be variably controlled. Accordingly, the variable range (i.e. tuning width of the transmission wavelength.lambda..sub.o) is the widest in the c-type filter although there is an upper limit in the refractive index .DELTA.n which is electrically variably controllable.
The a-type to d-type filters set forth above can transmit the light having the line width, i.e. transmission bandwidth extending .DELTA..lambda..sub.FWHM with the transmission wavelength as a center thereof. The line width .DELTA..lambda..sub.FWHM in the a-type filter to the d-type filter is expressed in the following formulas. ##EQU2## where L: length of the filter (length of electrode) R:reflectance at the plane of incidence and emittance
Since an inequality .delta.n&lt;&lt;n is normally established, the line width .DELTA..lambda.FWHM of the a-type, b-type and d-type filters is very narrow while the line width .DELTA..lambda.FWHM of the c-type filter is very wide as easily understood from the formulas (3a) to (3d).
The number of channels in the a-type filter is expressed as follows. ##EQU3## However, since it is subjected to the limitation of an FSR (Free Spectrum Range), the number of channels as a single element is expressed as follows. ##EQU4##
The number of channels in the b-type and c-type filters is expressed as follows. ##EQU5##
The number of channels in the d-type filter is expressed as follows. ##EQU6## where .DELTA..lambda.max is the maximum .DELTA.n in the variable
Accordingly, assuming that .DELTA.n.sub.max .perspectiveto.0.01 is established, the a-type filter has 10 channels by the limitation of the FSR provided that R 0.9 (capable of having 80 channels potentially if disregarding the limitation of the FSR). The b-type filter has 80 channels provided that L.perspectiveto.1 cm while the c-type filter has 8 channels provided that L.perspectiveto.1 mm and the d-type filter has 8 channels provided that L=500 .mu.m.
As mentioned above, the line width .DELTA..lambda..sub.FWHM can be narrowed but the tuning width (variable range of transmission wavelength .lambda..sub.o) can not be widened according to the conventional a-type, b-type and d-type filters. However, with the c-type filter the tuning width can be widened but the line width .DELTA..lambda..sub.FWHM can not be narrowed.
Accordingly, in view of increasing the number of the channels (=tunning width/line width .DELTA..lambda..sub.FWHM), the number of channels can be increased by lengthening the length L of the device which results in narrowing the line width .DELTA..lambda..sub.FWHM according to the a-type,b-type and d-type filters but it is difficult to use these filters if the line width .DELTA..lambda..sub.FWHM is narrowed. On the contrary, according to the c-type filter, it is impossible to increase the number of channels unless the length L of the device is lengthened to the extreme extent, e.g., L=1 m.